The purpose of this study is to present a simple hybrid approach for synthesizing heat exchanger networks (HENs). HEN structures are synthesized utilizing a genetic algorithm based on a modified node representation, which is very similar to the stage-wise superstructure model and allows for addressing the internal utility exchangers everywhere in the network. Although the model governing the continuous variables of each structure is non-linear, a relatively simple linear formulation is developed to handle these variables. This novel formulation consists of a linear programming model for maximum energy recovery, a linear correction procedure (COP), and two search loops. The COP focuses on finding the optimal values of exchangers' heat loads and stream split ratios in order to reach the minimum total annual cost of the network. Four extensively studied medium- to large-scale networks from the literature are investigated. Despite the simplicity of the proposed approach, comparing the results demonstrates its potential effectiveness.